Drag and Terminal Speed online LAB 5 (1) PDF

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Physics 211R: Lab Instructions

Drag and Terminal Speed (Newton’s Second Law) Reading Assignment: Knight: Chapter 6, Section 5 Introduction:

Photo by Keith Larrett http://www.webshots.com/ photos/skydiving1.html

Free fall is the situation when the only force acting on an object is the force of gravity: this includes an apple falling from a tree, a thrown baseball in the air, a satellite in orbit, and a person in midair during a jump. In some of these cases, however, free fall is only an approximate model for the motion of the object since an object moving through a fluid (including air) experiences a force called Drag that resists its motion relative to the fluid. So the net force acting on the object is not just gravity, but the vector sum of gravity (FG) and drag (D). While we often think of drag as a bad thing (e.g., it reduces a car’s fuel mileage), it also has its benefits: without drag, raindrops would fall as fast as bullets! While we often ignore the drag force in this course, in many circumstances this is not a reasonable assumption. (Solving problems with the drag force is much harder than problems without drag, so for a first course in physics, we usually omit it.) In this laboratory, however, we will see what effect air resistance can have on a system and explore some parameters that affect air resistance. We will assume that there is no wind and so the average velocity of the air molecules in the room is zero. The Drag force (sometimes called “air resistance” when the fluid is air) is a complex phenomenon caused by several different mechanisms. One mechanism is skin friction between the object’s surface and the fluid. Another mechanism arises from the fact that a thin boundary layer of the fluid attaches itself to the surface of the object; this boundary layer moves relative to the rest of the fluid and there is viscous drag acting on it (and thus on the object). This force usually depends on the velocity of the object moving in the fluid, the density and viscosity of the fluid, and size/shape of the object. (If you are interested in fluid physics, look up the term Reynold’s number after lab – it plays a large role in the Drag force and the conditions for turbulent fluid flow.) Depending on the relative magnitudes and directions of FG and D, the object may be accelerating or moving at constant velocity (a situation called terminal speed or terminal velocity). For example, a skydiver eventually reaches terminal speed after jumping out of a plane. Since our

insurance was cancelled after the last class “jump,” you will explore this phenomenon using pieces of paper.

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Physics 211R: Lab – Newton’s Second Law and Drag

Newton’s Second Law: Drag and Terminal Speed Conceptual Understanding Goals: By the end of this laboratory, you should be able to: (1) Describe a system using free-body diagrams and Newton’s Second Law. Drag relies straightforwardly upon the mass of the stream going past the airplane. The drag likewise depends in an unpredictable manner on two different properties of the air: its thickness and its compressibility. These elements influence the wave drag and skin erosion which are depicted previously. The drag power relies upon the square of the speed. So as the body speeds up its speed and the drag increment. ... At the point when drag is equivalent to weight, there is no net outer power on the item, and the speed increase gets zero. The item at that point falls at a steady speed as portrayed by Newton's first law of movement. (2) Determine the direction of the Drag force given information about the motion of the object. Drag of an object depends on dimension of the object. Hence drag on both sheet of paper and directory will be same. But Drag per unit mass of paper will be larger than that of directory ( since directory has greater mass). As we can see above accleration of object depends on negative of drag per unit mass hence accleration of paper will be less than that directory. Moe's case- If the smaller paper wasn't crumbled then drag per unit mass would have been same for both case and hence same accleration but crumbling reduces its area while mass remained same hence drag/mass decreased hence from above equation accleration of smaller piece was more. Curly: Since mass and dimension of both balls were same hence drag per unit mass of both will be same hence both will.

(3) Recognize constant velocity, constant acceleration, and variable acceleration motion from their velocity graphs. you learned in a previous module that speed is the pace of progress of position. Since dislodging is an adjustment of position, speed is additionally the pace of relocation. Uniform versus variable speed Past modules have managed uniform speed. Notwithstanding, numerous circumstances in life include variable speed and speed increase. For instance, the basic demonstration of halting a car at a traffic signal and afterward continuing the outing once the light becomes green includes variable speed and speed increase.

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Physics 211R: Lab – Newton’s Second Law and Drag

Three conditions I will clarify both of these subjects in this module utilizing three notable material science conditions that manage the removal of a shot in a vacuum affected by gravity . The condition that we will invest the most energy on is h = v0*t + 0.5*g*t^2 Speed increase Removal is an adjustment of position. Speed is the pace of progress of position or the pace of removal. Speed increase is the pace of progress of speed. Jerk is the pace of progress of speed increase (not canvassed in this module). As per this creator , there is no all around acknowledged name for the pace of progress of jer

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Physics 211R: Lab – Newton’s Second Law and Drag

(4) Describe the mathematical relationship between the drag force on an object and the object’s speed relative to fluid.

DRAG FORCE Drag force FD is found to be proportional to the square of the speed of the object. Mathematically

FD∝v2FD∝v2 FD=12CρAv2FD=12CρAv2, where C is the drag coefficient, A is the area of the object facing the fluid, and ρ is the density of the fluid.

Laboratory Skill Goals: By the end of this laboratory, you should be able to: (1) Demonstrate tenacity and patience required to carefully collect a “clean” set of data in a sensitive experimental setup. (2) Design an experiment to measure the motion of an object. (3) Draw reasonable conclusions about the motion of an object based upon data. Equipment List: Two pieces of paper (the same size) Timer Ruler, meter / yard stick, or measuring tape You will be doing three activities: Activity 1. Do a theoretical analysis of falling with drag force Activity 2. Do an experimental observation of falling with drag force Activity 3. Indirectly measure when terminal velocity is achieved. Lab Activity 1: Analysis of the Motion of an Object Falling in the Air Q1. You have three friends, Larry, Moe, and Curly, who each made an observation and then constructed a theory about falling objects from their observation: (1) Larry drops a flat sheet of paper and a Penn State directory, which are both about 8.5” x 11”. Larry observes that the directory falls a lot quicker than the paper. Thus, Larry deduces, heavier objects always fall faster than lighter objects. (2) Moe drops a whole sheet of paper and a small section of a piece of paper (which got crumpled up when he shoved it into his pocket). He observes that the smaller, and thus lighter, piece of paper hits the ground first. Thus, Moe deduces that lighter objects always fall faster than heavier ones.

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Physics 211R: Lab – Newton’s Second Law and Drag

(3) Curly drops a marble and a ping-pong ball from shoulder level and observes that both hit the ground at essentially the same time. Thus, he deduces that an object’s weight never affects the time an object takes to fall. Q1A. Draw free-body and acceleration diagrams for an object falling in the air. Do NOT neglect drag (“air resistance”). From these diagrams write Newton’s Second Law for the object. Finally, solve for the acceleration of the object in terms of the drag force D, the mass m, and g. Drag of an object depends on dimension of the object. Hence drag on both sheet of paper and directory will be same. But Drag per unit mass of paper will be larger than that of directory ( since directory has greater mass). As we can see above accleration of object depends on negative of drag per unit mass hence accleration of paper will be less than that directory. Moe's case- If the smaller paper wasn't crumbled then drag per unit mass would have been same for both case and hence same accleration but crumbling reduces its area while mass remained same hence drag/mass decreased hence from above equation accleration of smaller piece was more. Curly: Since mass and dimension of both balls were same hence drag per unit mass of both will be same hence both will

Q1B. What explanation would you give to Larry, Moe, and Curly that would account for all of their observations? Be as complete and detailed as possible (just tossing out vocabulary words doesn’t explain anything). Think about what the drag force might depend on and use your above expression for acceleration in your explanation. Drag relies straightforwardly upon the mass of the stream going past the airplane. The drag likewise depends in an unpredictable manner on two different properties of the air: its thickness and its compressibility. These elements influence the wave drag and skin erosion which are depicted previously. The drag power relies upon the square of the speed. So as the body speeds up its speed and the drag increment. ... At the point when drag is equivalent to weight, there is no net outer power on the item, and the speed increase gets zero. The item at that point falls at a steady speed as portrayed by Newton's first law of movement.

Larry: Why did the phone book fall faster than the sheet of paper? Because the weight of phone book is higher than a sheet of paper . Moe: Why did the crumpled paper fall faster than the heavier flat sheet? when the piece of paper was folded, they hit the ground simultaneously! ... At the point when the paper is smooth, it uncovered an enormous surface to the air underneath it which eases back its plummet. Whenever it is folded, the surface which interacts with the air is a lot more modest, permitting it to fall a lot quicker. Curly: How could the two balls have fallen at about the same time?

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Physics 211R: Lab – Newton’s Second Law and Drag

At the point when you drop a ball (or anything) it tumbles down. Gravity makes everything fall at a similar speed. This is the reason balls that weigh various sums hit the ground simultaneously. Gravity is the power acting in a downwards heading, yet air opposition acts in an upwards course

Q2. Carefully draw the velocity (VD), free-body (FBD) and acceleration (AD) diagrams for an object being dropped from rest in the air and reaching terminal speed, at three points in time: (a) immediately after being released (b) some time later but before reaching terminal speed (c) after reaching terminal speed. Make sure the vectors in each diagram show their relative scale. Using a double-line arrow (=>) to distinguish it from the individual forces, draw the vector sum of forces (net force). Moment of release VD

FBD

Before Terminal Velocity AD

After Terminal VD

FBD

VD

FBD

AD

Q3 Ball thrown up AD

VD

FBD

AD

Q3 What would the free-body and acceleration diagrams for a ball being thrown upwards look like? (Draw above)

Q4. Write Newton’s Second Law for the object in case (b) after release but before reaching terminal speed. (You can choose either up or down as your positive direction of your coordinate system; just be clear to state which choice you have made.) Describe how Newton’s Second Law for cases (a) and (c) differs, if at all, from the equation you have written.

Newton's subsequent law says that the speed increase and net outer power are straightforwardly corresponding, and there is a contrarily corresponding connection among speed increase and mass. For instance, an enormous power on a minuscule item gives it a gigantic speed increase, yet a little power on a tremendous article gives it almost no speed increase. Likewise, power and speed increase are a similar way.

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Physics 211R: Lab – Newton’s Second Law and Drag

The condition for Newton's subsequent law is: F=ma with, vector, on top, approaches, start part, \Sigma, F, with, vector, on top, separated by, m, end portion, rises to, start division, F, with, vector, on top, start addendum, start text, n, e, t, end text, end addendum, partitioned by, m, end division We can likewise revamp the condition to tackle for net power: \Sigma\vec F = m\vec aΣF=ma\Sigma, F, with, vector, on top, approaches, m, a, with, vector, on top Where \vec aaa, with, vector, on top is speed increase, \Sigma\vec FΣF\Sigma, F, with, vector, on top is the net outer power, and mmm is mass of the framework.

Q5. Your two laboratory partners are having a discussion about the free-body diagrams. Your first partner argues, “The drag force can never be as large as gravity, even at terminal speed, otherwise the object would stop in mid-air.” Your second partner argues, “The drag force must be larger than gravity at terminal speed since it needs to overcome gravity to make the object stop accelerating downwards.” How do you resolve this discussion in your group?

The power on an item that opposes its movement through a liquid is called drag. At the point when the liquid is a gas like air, it is called streamlined drag or air obstruction. At the point when the liquid is a fluid like water it is called hydrodynamic drag, however never "water obstruction". Liquids are described by their capacity to stream. In fairly specialized language, a liquid is any material that can't avoid a shear power for any obvious timeframe. This makes them difficult to hold however simple to pour, mix, and spread. Liquids have no unequivocal shape except for assume the state of their holder. (We'll overlook surface strain for the present. It's truly just critical on the limited scale — little like the size of a drop.) Fluids are pleasant it might be said. They yield their space moderately effectively to other material things; in any event when contrasted with solids. A liquid will move on the off chance that you ask it. A strong must be advised to move with ruinous power.

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Physics 211R: Lab – Newton’s Second Law and Drag

Liquids may not be strong, however they are definitely material. The fundamental property of being material (in the old style sense) is to have both mass and volume. Material things oppose changes in their speed (this is having mass) and no two material things may consume a similar space simultaneously (this is having volume). The segment of the drag power that is because of the idleness of the liquid — the obstruction that it needs to being shoved aside — is known as the pressing factor drag (or structure drag or profile drag). This is typically the thing somebody is alluding to when they talk about drag. Review Bernoulli's condition for the pressing factor in a liquid… P1 + ρgy1 + ½ρv12 = P2 + ρgy2 + ½ρv22 The initial term on each side of the condition is the piece of the pressing factor that comes from outside the liquid. Regularly, this alludes to environmental pressing factor burdening the outside of a fluid (not applicable at the present time). The subsequent term is the gravitational commitment to pressure. This is the thing that causes lightness (likewise not important at the present time). The third term is the motor or dynamic commitment to pressure — the part identified with stream (important at this moment). This will assist us with understanding the starting point of pressing factor drag. Start with the meaning of pressing factor as power per region. Tackle it for power. P=

F

⇒

F = PA

A Substitute the conventional image F for power with the more explicit image R for drag. (You could likewise utilize D on the off chance that you needed to.) Drop in Bernoulli's condition for the pressing factor in a moving liquid…

Q6. Looking at your four free-body diagrams, what patterns do you see in terms of the direction and magnitude of the drag force D and the velocity v? Free-body graphs are charts used to show the general extent and course of all powers following up on an article in a given circumstance. A free-body graph is a unique illustration of the vector charts that were talked about in a prior unit. These graphs will be utilized all through our investigation of physical science. The size of the bolt in a free-body chart mirrors the greatness

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Physics 211R: Lab – Newton’s Second Law and Drag

t

of the power. The course of the bolt shows the bearing that the power is acting. Each power bolt in the chart is marked to show the specific kind of power. It is by and large standard in a freebody outline to address the item by a case and to draw the power bolt from the focal point of the crate outward toward the path that the power is acting. An illustration of a free-body graph is appeared at the ok

Q7. From your free-body diagrams, will be experiencing constant

make an argument about whether the object falling acceleration motion before it reaches terminal speed.

Q8. Sketch an acceleration-time graph

for the object.

point!

a

Check with an instructor at this

Lab Activity 2:

Experimental Observation of an Object Falling in the Air

t

Now you are ready to see what the motion of a falling object looks like and how drag plays a role in fall time. In this case you will investigate 2 objects. A tightly crumpled up ball of paper, and a mostly open piece of paper. The goal of this experiment is 1. To determine if the ball of paper feels a drag force by measuring its fall time vs height of drop and comparing it to free fall. 2. To determine the terminal velocity of the open paper by measuring the fall time vs height of drop.

Q9. Based on Activity 1 above, the ball of paper and the open

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what do you think the acceleration vs time graph will be for piece of paper. Label them on the graph below.

Physics 211R: Lab – Newton’s Second Law and Drag

a Q10. Write an expression for the time t it will take the ball to fall as a function of drop height h, assuming no drag (free fall):

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Physics 211R: Lab – Newton’s Second Law and Drag

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Physics 211R: Lab – Newton’s Second Law and Drag

Q11: The paper was dropped from height h above the ground, took a time tdrag to reach terminal velocity, and reached terminal velocity at height hdrag above the ground. In terms of those parameters, how long a time does it take the paper to reach the ground?

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Physics 211R: Lab – Newton’s Second Law and Drag

Q12. Explain how you will do your experiment below. In practice the speed that objects fall may vary, because air resistance will act on objects pushing them up slightly, in opposition to gravity. The greater the surface areas of an object the more surface for air to push up against and so air resistance will act upon a falling object, slowing i...